Feedforward attractor targeting for non-linear oscillators using a dual-frequency driving technique

Abstract

A feedforward control technique is presented to steer a harmonically driven, non-linear system between attractors in the frequency-amplitude parameter plane of the excitation. The basis of the technique is the temporary addition of a second harmonic component to the driving. To illustrate this approach, it is applied to the Keller-Miksis equation describing the radial dynamics of a single spherical gas bubble placed in an infinite domain of liquid. This model is a second-order, non-linear ordinary differential equation, a non-linear oscillator. With a proper selection of the frequency ratio of the temporary dual-frequency driving and with the appropriate tuning of the excitation amplitudes, the trajectory of the system can be smoothly transformed between specific attractors; for instance, between period-3 and period-5 orbits. The transformation possibilities are discussed and summarized for attractors originating from the subharmonic resonances and the equilibrium state (absence of external driving) of the system.

Enhancing cavitation dynamics and its mechanical effects with dual-frequency ultrasound

“…It should be noted that the period number of lower frequency is used for the dual-frequency case, similar to the previous study (Wang et al 2021). Actually, the amplitude of dualfrequency ultrasound is modulated by the two single-frequency components (Yeh et al 2009, Guédra et al 2017, Law and Zhou 2018, Suo et al 2018, Zhou and Lei 2020, thus the dual-frequency driving is still periodic and its period can be calculated as the method described in the previous study (Hegedűs et al 2020). In our simulations, the calculations were performed during five periods of the dual-frequency ultrasound.…”

“…Note that the larger the peak negative acoustic pressure is, the larger the bubble expansion becomes. For the same energy input, the peak negative acoustic pressure dual-frequency ultrasound could be larger than that of each single-frequency ultrasound ( P PNP ∆ > 0), which is conducive to enhance the bubble cavitation and its associated bio-effects (Yeh et al 2009, Hegedűs et al 2020. Therefore, the frequency ratio and the phase difference between the two components can be reasonably chosen to maximize the peak negative acoustic pressure of the resultant dual-frequency ultrasound, thereby achieving an obvious enhancement of the bubble dynamics.…”

Solving large number of non-stiff, low-dimensional ordinary differential equation systems on GPUs and CPUs: performance comparisons of MPGOS, ODEINT and DifferentialEquations.jl

“…It is a non-linear second-order ordinary differential equation. In order to remain consistent with our previous publications [44,91,92], the dual-frequency version is employed. The system reads as…”

GPU accelerated numerical investigation of the spherical stability of an acoustic cavitation bubble excited by dual-frequency

“…It must be emphasized that from the available program packages, at the moment, MPGOS has the best performance for solving a large number of non-stiff, low-dimensional ordinary differential equations on GPU [88] , [89] . The capabilities of GPU-accelerated initial value problem solvers has already been demonstrated in papers [90] , [91] , [92] .…”